Towards the end of the 1930s, along with Keres and Capablanca, Eliskases was regarded as a potential contender for a World Championship encounter with Alexander Alekhine. Indeed, Alekhine spoke out in favour of a match with the Austrian, who had acted as a second during his successful attempt to regain the title from Max Euwe in 1937.

However, Eliskases' defection to South America was badly timed, as documentary evidence later showed that the Nazi regime had scheduled him a 1941 match with the World Champion, but due to circumstances, had subsequently abandoned the idea. In terms of his credentials for such a contest, he was one of very few masters and certainly the only Austrian to have beaten three world champions (Capablanca, Euwe and Fischer). Indeed, he had a plus score against Euwe (3-2),[1] and even scores against Capablanca (2-2)[2] and Fischer (1-1).[3] Eliskases' critics may have pointed to the impressive credentials of Keres, his main rival, but the Estonian too had twice fallen victim to Eliskases in tournament play.

He was considered an expert in the endgame—at Semmering 1937, he outplayed and beat Capablanca in this phase, despite this being the forte of the Cuban ex-world champion. Dutch grandmaster Hans Ree observes that Eliskases is one of only four players (Keres, Reshevsky and Euwe being the others) to beat both Capablanca and Fischer.